You don't give the flights or airline(s) involved, so giving you anything more than general information won't really do you any good.
If you are on the same itinerary the airline should transfer your bags automatically to your International flight. Also, not all International Flights leave from the "International"(Tom Bradley International Terminal). So there is a chance that you will arrive and depart in the same terminal.
The airport is shaped in more of a Horseshoe, with TBIT being at the top. T1-T2-T3-TBIT-T4-T5-T6-T7-T8. As a rough estimate figure about 5 minutes between each terminal, so to get from say Terminal 2 to TBIT figure about 10 minutes. If you don't want to walk you can take the Terminal Shuttle that you can catch on the Arrivals Level.
Going between Terminals will generally(but not always require you to go through security again), such as going between T5 & T6. But if you do have to switch terminals and do have to go back through security you need to allow yourself about an hour.
So if your bags are checked through, you should have plenty of time to get to your next flight. If you do have to get and recheck your bags that could add another hour easily to this process and there would be a good chance you would miss your flight. Especially if the flight is late.
EDIT: If all of your tickets and flights are separate you need more time. Because they are separate if your first flight is late enough and you miss the second flight. There is a possibility that you would just loose that ticket or have to pay a penalty to try to get on another flight.
So it would be best to plan to arrive the day before and spend the night. This way even if your first flight is delayed you should still be able to get there in time for the 2nd flight. If that is not an option, you need to allow yourself at least 4-5 hours. If you are trying to book a flight this way to save money..think about if the savings is worth the possibility that you may miss the 2nd flight.
JetBlue Flies into T3, and Air New Zealand operates out of T2. So you will have to get your bags from JetBlue, walk to T2, Drop your bags at Air New Zealand and go back through security. So the above times pretty much stand. The MINIMUM you should allow yourself is 4-5 hours, but to handle possible delays coming in the day before would be best.